01.42
"I define knowledge as a relation between two or more concepts, where concepts are mental objects. But these concepts do not exist apart from a conceptualizer, an intelligent being. Thus human knowledge is subjective and has no absolute meaning."
-- Patrick Reany
"Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world.
In our endeavor to understand reality we are somewhat like a man trying to understand the mechanism of a closed watch. He sees the face and the moving hands, even hears its ticking, but he has no way of opening the case. If he is ingenious he may form some picture of a mechanism which could be responsible for all the things he observes, but he may never be quite sure his picture is the only one which could explain his observations. He will never be able to compare his picture with the real mechanism and he cannot even imagine the possibility or the meaning of such a comparison"
EVOLUTION OF PHYSICS
by Albert Einstein, Leopold Infeld
Touchstone, 1938, p31.
"A human being is a part of the whole, called by us "Universe," a part
limited in time and space. He experiences himself, his thoughts and feelings
as something separated from the rest a kind of optical delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest to us.
Our task must be to free ourselves from this prison by widening our circle of compassion to embrace all living creatures and the whole of nature in its beauty. Nobody is able to achieve this completely, but the striving for such achievement is in itself a part of the liberation and a foundation for inner security. "
-- In H. Eves Mathematical Circles Adieu,
Boston Prindle,Weber and Schmidt, 1977.
What is Knowledge?
by Patrick Reany
Published in: Arizona Journal of Natural Philosophy, Vol. 2, March 1988, pp. 7-14.
Copyright 1988 by Patrick Reany. All Rights Reserved.Reprinted with permission.
The detailed answer to the question "What is knowledge?" is of central importance in the enquiry of epistemology. This essay will be only an introductory answer to the following two questions:
- In what sense does knowledge exist?
- What is the relation of knowledge to truth?
To answer these two questions we must first investigate the general process by which we attain new knowledge.
When we talk about knowledge what we mean is knowledge about some object. Informally, knowledge is a description of the state of some object. The object may be either physical or abstract. Some examples of abstract objects include love, hate, memory, the future, and even knowledge itself. We naively believe that our knowledge of reality is direct, but this is a mistake. Our experience with physical objects is actually indirect. We do not directly mentally experience physical objects; we mentally experience only our concepts of them.
I define knowledge as a relation between two or more concepts, where concepts are mental objects. But these concepts do not exist apart from a conceptualizer, an intelligent being. Thus human knowledge is subjective and has no absolute meaning. However, we may postulate the existence of an all-knowing, eternal, perfect God that acts as an absolute standard of knowledge and truth, and though there are many reasons to do this we must admit that any definition of an absolute standard is both subjective and logically arbitrary.
I have been trying to convey the idea that knowledge has a different kind of existence than matter. For even if we allow that matter has an existence independent of intelligence, we cannot say the same for knowledge. Knowledge is very much like sound and color. When a tree falls in the forest it is assumed to make a lot of sound waves, but if there is no creature nearby capable of hearing, then it makes no sound. Likewise, when light reflects off an object it produces characteristic wavelengths of light, but neither the object nor the light are colored in themselves. Color exists in the mind of the perceiver. Color and sound are the brain's method of making sense out of external signals picked-up by our sensory organs. In like manner, knowledge does not exist without a knower, and there is no such thing as "unknown" knowledge.
This brings us to consider in more detail the process of obtaining knowledge. To that end I offer my own simplistic view. Sometime after conception, the normal fetus develops the rudiments of a Knowledge Formation System, or KFS. The KFS has two major parts: the Semantic Analysis System (SAS) and the Program Enhancement System (PES). By analogy to artificial intelligence, the SAS is both “software” and “hardware” that functions to convert raw sensory data, carried to the brain via the nervous system, and there produces meaningful concepts about the outside world (i.e., the world “outside” of human consciousness). The PES serves to improve the SAS. Thus the human is like a computer and programmer in one, though this should come as no surprise. We could define the efficiency of the PES as a measure of intelligence. If we do, however, it seems inescapable that intelligence is largely a function of erudition, open-mindedness, curiosity, and mental stamina, which puts intelligence under the category of a developmental skill. If I may speculate some more, I believe that intelligence (the efficiency of reprogramming) is a decision process which uses value judgments to choose “good” programming criteria out of assorted criteria. This process is called the “philosophy” of programming. My induction here, also bolstered by my own experience, is that efficient reprogramming is aided immensely by general philosophical know1edge and contemplation.
In brief, the SAS works by intercepting sensory signals, converting these to appropriate nervous impulses that are sent to the brain (this part I refer to the lower SAS), and there these impulses are transformed into meaningful concepts that the mind can use to compare against similar concepts stored in memory (M) This functional part I refer to as the higher SAS. Thus, new knowledge is created by relating the new concepts to the old. By the way, when the human mind is engaged in “pure abstract thinking,” the meaning given to new abstract concepts will also be in terms of old concepts, both “purely” abstract and not. If all goes well, the new knowledge is stored in M.
It is logical to infer from this theory that the fetus, in order to use the KFS when it is in place, must have access to a priori, nontrivial concepts in M ready to be used by the KFS for making comparisons. This inference has been debated for hundreds of years. I call these a priori concepts archephors, on which metaphors of new knowledge are originally built. In this theory of human learning, meaning is more fundamental than knowledge, for knowledge is conformed to and limited by our ability to project meaning onto the world, and all meaning is ultimately reducible to the undefinable archephors.
In human terms, I cannot conceive of a good definition of absolute knowledge. We think of knowledge as being like the objects it represents. Thus knowledge is a metaphor for these objects and their purported relationships. Written knowledge, being a metaphor for mental knowledge, is once removed from "pure abstract" thinking, and twice removed from the physical, spiritual, and occult realms.) I shall content myself only to discuss the relation of knowledge to the concept of truth. In other words, of all that is called knowledge, what part of it is an accurate description of the way things really are? To avoid an obvious infinite regression, the best we can hope to decide on this is just what we believe, not what we know, is true about knowledge. Our criteria for belief may include experimentation, appeal to authority, consensus, and intuition. But how can anyone say definitively that one criterion is better than any other? Such is a value judgment. Even the putatively most objective among us, the scientist, is for example inclined to believe in causality which has no rational basis for one to believe in its existence: causality is not an observable. Belief in causality is indeed irrational, but it is also instrumental for mentally modeling the physical realm, and such modeling has proven to be useful.
The fundamental problem in believing in absolute knowledge is found in the dichotomy between what is and how we characterize what is, which in philosophical terminology is the difference between metaphysics and epistemology. For the sake of argument, say that we grant that matter exists in some kind of Absolute state. How we characterize that state depends on our habits of reasoning, our particular mode of experiencing the physical realm through our senses, and our requirement to found all characterizations on arbitrary definitions. We have no way to defend beyond all doubt the way we reason, i.e., the logic we adhere to. In fact, from Eastern mysticism to Zeno's Paradoxes to Quantum Mechanics we find grounds to doubt the infallibility of so-called Western logic. Ultimately, barring the use of intuition and revelation, our only means of characterizing the world is through our SAS. It seems to do a fair job in helping us deal with the world, but that's no guarantee that there are no other sentient beings with radically different sensory capabilities and SAS that can also deal effectively with the same world. We cannot prove that our way of forming characterizations of the world through the SAS is absolute, so we cannot prove that the definitions we adopt to characterize the world in accordance with the SAS are absolute. For example, we define Euclidean space and distance as a means of characterizing the world simply because those definitions help to maximize the meaning of the mental images provided to us by our naturally Euclidean SAS. But that any meaning of length is considered necessary to know the “absolute” nature of the world is itself a value judgment!
Even after deciding to use lengths as a characterization of the world, we are still faced with decisions about the choice of a unit length and the invariance of length under physical transportation of our standard. Furthermore, we accept as an arbitrary definition that rulers demonstrated to be congruent to the standard remain so when they are removed from the standard. (There is no physical test for congruence of separated rods that does not involve unwanted assumptions about space, time, and light propagation. ) Not only is congruence itself an arbitrary definition, but the means to determine congruence is based ultimately on human perception: There is no independent means to know if we humans properly follow our own definition of testing congruence in practice. (Please give this proposition some serious thought.)
Now for an example of the arbitrariness of our definitions, consider two ways to measure the height of a horse. We can measure up to so many “hands” as is traditional, or we can be more “accurate” by using a meter stick. Not only are the two methods not even equivalent to within a scale factor, but we must seriously question the implied bias of stating that one is more accurate than the other. The question is “more accurate for what purpose”? We choose our definitions as we do because they are useful to us, but usefulness is subjective. What we need in the search for absolute knowledge is a system to characterize the world in which we simply have no choices to make about how to do it. Thus we are led to this fundamental question: How can absolute knowledge be based on arbitrary definitions? It seems clear to me that it can't.
Thus even if absolute knowledge exists in some form, it is not yet available to man except by revelation or intuition, in which case we can still choose to accept or reject it. It is often said that absolute knowledge of physical objects exists, such as absolute lengths of rods, and that we can know “approximate” absolute knowledge by taking accurate measurements. If we increase the accuracy of the measurement, we increase the closeness to absolute knowledge. Whereas I might agree that for practicality more accurate measurement may provide a “better” measure of an object, I do not agree that it brings us any closer to absolute (i.e., exact) knowledge. Just what is this implied metric on knowledge by which we can supposedly judge the “closeness” of two pieces of knowledge? For all we really know, absolute knowledge, if it exists at all, is a hit-or-miss proposition, where a miss is as good as a mile. In short, how do we know that absolute knowledge is even capable of approximation? Isn't the very term “approximate Absolute” an oxymoron?
Human knowledge is a subjective means of coming to grips with the world. As far as we can prove, human knowledge never captures the essence of reality; it merely characterizes it according to our own purposes. In an ironic sense we are epistemologically blinded to reality by our own senses, which we take to be indicators of an absolute, independent world. Before we can judge the truth or falsity of a proposition, we must first be given a proposition that makes sense to us. In fact, it is hard to believe that a proposition that doesn't make sense is really a proposition at all. Here's the point. Assume for the sake of argument that there are absolute “fundamental realities” out of which all the universe is composed.
Suppose further that our sensory system can detect, codify, and transmit to the brain impulses that correspond in one-to-one fashion to these fundamental realities. Now what if, to make sense out of the farrago of sensory signals the SAS encounters, the brain must unify (synthesize by interpretation) some of these fundamental realities (being represented by impulses) into a composite that the mind falsely interprets as a nonreducible thing, and it must analyze (reduce by interpretation) some fundamental realities into meaningful, but false, “more” fundamental realities. The first I call the fallacy of unjustified synthesis and the second the fallacy of unjustified reduction. An example of the latter may be one of Zeno's paradoxes of motion, where he argued that it is logically impossible to move from a given point to any other point because there one must first traverse half of that distance, and also half of that half, and half of that half, and so on. There being always some subinterval to accomplish before motion can begin, then motion is impossible, or so Zeno would have us believe. Apparently it never occurred to Zeno to doubt the assumption made here that any interval is capable of arbitrary, let alone infinite, subdivision. We have today every reason to believe that the world is not arbitrarily divisible into “parts.” Though we still may be able to keep the adage “A total is equal to the sum of its parts” if we realize that the reduction to “parts” must not be arbitrary, i.e., must not be accepted merely because it is capable of mental conception.
I have argued in this essay that the first requirement of the SAS is to produce meaning out of sensory chaos, and that in doing so we may pay the price of distorting “reality.” For better or for worse, we are stuck with the SAS that we have. So we should become aware of its possible shortcomings in presenting the mind with a true representation of reality. Not only are we probably given a distorted view of reality, as in the case of the moon illusion in which the moon appears larger as it looms just above the horizon than when it is overhead, but we know that the SAS is incapable of detecting many forms of known signals, and who knows how many unknown ones. Unless our SAS can “make sense”" out of the raw sensory data it receives, that sensory data will never be interpretable to us as knowledge at all. This situation is much like that of the mathematics student trying to understand abstract algebra. The problem his SAS is faced with is to make sense out of an abstract (i.e., purely syntactical) system which is defined by abstract axioms referring to all “objects” capable of fulfilling the axioms. The only way the student can make sense out of such a system is to become familiar with one or more particular examples of the system. Thus, in learning the examples he transfers meaning to the abstract system. It remains an open question, however, whether one ever understands an abstract system by this or any other method, or rather whether one just becomes adept at working with it.
An interesting question here is the discovery of so-called analytic knowledge. Analytic knowledge is knowledge that is deducible from a body of facts by deductive reasoning. A Kantian example of true analytic knowledge is the truth of the statement “All black cats are black” because the predicate black is explicitly contained in the logical subject black cat. It has been asserted that since computers can reason deductively that they should be capable of proving all the known theorems, say of group theory, by just being given the axioms of the theory. Although computers have done well in lesser areas, such as in proving the theorems of the predicate calculus, I do not believe they are up to the challenge of group theory. For a number of years now I have pondered the intriguing question of where mathematical theorems come from. For example, the enormous body of theorems in group theory seems out of proportion to the four axioms that found group theory. Where did all these theorems come from? The detailed answer to this question should aid in the search for new theorems, whether by man or by artificially intelligent machines (AIMs). A theorem is a set of deductive steps, each of which is justified by an axiom, a previously proved theorem, a given, or a definition. The purpose of given conditions is to specify a particular structure to be investigated, and the purpose of definitions is to specify (possible) properties that a particular system may have. Now, an obvious question to a mathematician is whether the group identity is unique. But would a machine know to formulate that question? The notion of uniqueness is not explicit in the axioms of group theory, yet it is provable that the identity element is indeed unique for every possible group. Thus, unless I'm quite mistaken in my reasoning, the fact that the identity is unique is not analytically contained in the axioms of group theory. (Thus I believe that this case is a legitimate example of Kant's so-called synthetic a priori knowledge.) Perhaps we need to rethink what we mean by an abstract system in mathematics. Perhaps we should explicitly define not only the axioms of the system, but also al1 the possible definable properties (given by standard definitions) that the system is going to use. But such a procedure seems absurd, and where is the allowance for brand new definitions to arise, as was the case in group theory with the introduction of the terms “normal subgroups” and “quotient groups”? But how could an AIM, let alone a deductive computer, intuit the notion of quotient groups? Does artificial intelligence require artificial intuition? In an unnerving sense, subgroups and quotient groups exist because mankind has a propensity for inventing order out of chaos. Subgroups and quotient groups are groups found within other groups, and that's a very satisfying invention to the human side of mathematicians. When mankind looks at the random stars he invents order by “seeing” patterns that aren't really there; in Western civilization we called these patterns constellations. But when an AIM looks at the stars will it ever “see” anything other than random points of light? I have stressed the term “invent” because, for infinite groups anyway and lacking a surefire method to prove the consistency of axioms + givens, the theorems of such groups are not ultimately deductive and analytic as they appear: their ultimate justification lies in intuition. (Perhaps the dichotomy between Kantian analytic and synthetic knowledge is the dichotomy between “rigorous proof” and “proof by intuition.”)
We are about to encounter some philosophical terms whose definitions are nonstandard to common usage, dictionary definition, and scientific acceptance. (Philosophical terms are notorious for this.) The term “rationalism” I particularly want to address. In philosophical circles, rationalism means to deduce factual knowledge from a priori premises, that is, from premises that are somehow known to be “true” prior to observing the world. Dual to rationalism is empiricism, which is the deduction of factual knowledge from a posteriori premises, that is, from premises that are knowable only by observing the real world. One very good reason that scientists do not accept either of these extremes is that the scientific method uses both kinds of deduction. I will chance suggesting a revision of labels in this matter. The common connotation of rationalism is the ability to deduce (rationalize) truth about the world from a set of premises, regardless of the status of the premises, so long as they are judged to be true. Now if “true deductive knowledge” always requires the set of premises to be either 1) a priori true, then I shall refer to it as classic rationalism, or 2) a posteriori true, I shall refer to it as classical empiricism. To me, the major problem with rationalism is its insistence that its knowledge is “truth about the real world” rather than just “useful beliefs about appearances.”
The fallacy of deductive reasoning as a “truth preserving” operation strikes a fatal blow at the foundations of the many forms of so-called rationalism. The Rationalist movements were and still are an attempt to present knowledge as a true representation of reality. These movements have all claimed to present their views as independent of human vagaries and subjectivity - putting it in the third person, sotospeak, and attempting to speak for all “rational” people. In writing, the use of the third person has its use, particularly in exposition of mostly “factual” material. But in the presentation of controversial matters, such as in an essay, the use of the third person form is more often than not an affectation, a pretense at objectivity. I say this because human knowledge is actually one great essay of human opinion. For even if every human alive should agree, for example, to measure lengths of rigid rods by one operational definition only, that still does not remove the logical arbitrariness and theoretical controversialness of that definition. Besides that, as I have stated before, that “lengths” have any importance at all in characterizing the so-called absolute nature of the world is a value judgment.
In her book Introduction to Objectivist Epistemology (1966, Mentor, New York), Ayn Rand champions the cause of promoting objective knowledge; that is, that man can perceive reality and see it as it “really” is. Hers is a form of rationalism, though she is quick to denounce other forms of rationalism. I just wish that Rand and all other rationalists would he as objective in analyzing the arbitrariness, subjectivity, and uncertainty of the foundations of any human epistemology. A valid logical argument is only as good as its premises. For the valid argument to be sound, all the premises must be true. Now there are effectively only three ways that a premise can be true. Either a premise is logically true (i.e., it is true by the adoption of an arbitrary linguistic convention, such as the statement “all black unicorns are black,” which has no particular reference to blackness or unicorns), or it is true by some other deductive reasoning, or it is true by a human judgment (including arbitrary definitions). The role of human judgment in deciding truth is inescapable. Consider the proposition that a real person named George Washington was our First President (or at least hardly anybody) doubts this, yet as Bertrand Russell pointed out, it could be that the universe was created just five minutes ago, and we all have false “memories” of prior events. Since no one can disprove Russell's proposition, then we must doubt to some degree all of so-called history. Would the rationalists and the objectivists retort that for practical purposes, even if Russell's proposition was true, we can all go on in life as though it was false, for the appearance of the truthfulness of our common beliefs in history is all we really need? But this line of argument is pragmatic not absolute as the rationalists and the objectivists portray.
Rand vehemently rejects the notion that man's knowledge is based on arbitrary definitions. But consider this example of a categorical syllogism:
All A is B and all B is C, therefore all A is C
This syllogism, like all categorical syllogisms, is completely formal and devoid of meaning. Any meaning given to it must come by extension from its particular cases of applicability. But who decides which cases are applicable, and by what criteria do they decide this? Most of us agree that the following is a proper particular example: Box A is completely inside box B and box B is completely inside box C therefore box A is completely inside box C. But to point to this case, or any other case, and declare it as a proper categorical deduction is a value judgment. And consider the role of human intuition regarding “insidedness” used in deciding this proposition. We arbitrarily have decided to decide the uses of categorical syllogisms strictly on the basis of what the words we use in them mean to us, which is subjective. But which is it? Do the syllogisms themselves define the meanings of the terms they imply, or do the meaning and applicability of the syllogisms devolve from the meanings of the terms?
It seems ironic to me that I can find one of the best apologetics for my own position on knowledge from Ayn Rand's own writings to debunk it (1966, 10):
It is here that Protagoras' old dictum may be given a new meaning, the opposite of the one he intended: “Man is the measure of all things.” Man is the measure, epistemologically - not metaphysically. In regard to human knowledge man has to be the measure, since he has to bring all things into the realm of the humanly knowable....
Rand immediately goes on to deny that this leads to subjectivism, but I cannot disagree more. We ought to just be happy that we can find any useful means of characterizing the world by mental constructs; instead, however, we arrogantly believe that because we found one way to do it that must be the absolute way to do it. Rand's finesse has backfired. Not only does her metadictum support subjectivism, but it shows that the world we know it is an anthropomorphic extension of ourselves. We demonstrate our own self-hypnosis in, believing in the “objective ‘out there’ ” every time we forget that objects are not colored, that objects are not intrinsically near or far, sweet or sour. In all these things we project our own feelings onto the world. I am not arguing against this anthropomorphism, mind you (it has fortuitously served us very well up to this point) I'm just saying that we ought to admit that we are doing it, and admit that knowledge is subjective.
As best as I can figure, Rand identifies irrationality and unreason with mysticism (Rand, 1982, Philosophy Who Needs It?, Signet, New York, 62)
What is mysticism? Mysticism is the acceptance of allegations without evidence or proof, either apart from or against the evidence of one's senses and one's reason. Mysticism is the claim to some non-sensory, non-rational, nondefinable, non-identifiable means of knowledge, such as “instinct,” “intuition,” “revelation,” or any form of “just knowing.”...
I repeat: Reason is the faculty which perceives, identifies and integrates thematerial provided by man's senses. Mysticism is the claim to non-sensory means of knowledge.
It seems implicit in this argument that we must choose once-and-for-all between rational/sensorial knowledge and nonrational/nonsensorial knowledge. I do not do that, and I think few are willing to, either. I think that most of us follow what I refer to as Genericism - the use of many diverse epistemologies to decide on truth, beliefs, and commitments. Genericism is more open-minded, less dogmatic but it also demands more from its followers, who must actively weigh the relative merits of one epistemology against all others, or one person's rationality or irrationality against all others. Rand seems to regard science as the perfect example of the fruits of rationality, yet she seems oblivious to Hume's refutation of a rational science being based on induction and causality. Physical laws, being mere inductions, are no better than statements of faith, no matter how much evidence is given for past successes. Furthermore, much of what is considered scientific truth is mere implication on nonsensory data, such as the inference in “atomic energy levels” based on the measurement of spectral emissions from atoms. But even more can be said of this example, for even our instruments do not directly “sense” energy levels, only emission frequencies. Belief in invisible atomic and subatomic order, structure, and causality is an anthropomorphic extension of these concepts as applied to personal and social laws, structures, and interrelations.
Rand is also oblivious to the arbitrariness of defining a sharp distinction between what is rational and what is not. It's like the difficulty of defining a boundary between the ocean and the beach, or like the difficulty in defining the boundary between the natural and the supernatural. We cannot just say that the nonrational is whatever is not rational until we first provide an unequivocal definition of “rational.”
Now I wish to illustrate the fact that deductive reasoning is ultimately based upon unjustifiable faith, or as Rand puts it: just knowing. Try this experiment: Take any proposition that YOU feel strongly about; I will use the case of the peaceful use of nuclear energy. Take a stand on it one way or the other. Now give a justifying reason for the stand you took. Now also justify that reason, and continue this regression until you arrive at a reason that you cannot justify in words by rational argument. When you have done this, you will have consciously discovered the innermost driving force to your life: your personal core of heart-felt beliefs. In the case of the peaceful use of nuclear energy, I decided that, until renewable energy sources are available at low cost, the peaceful use of nuclear energy is good because it is good for mankind's over all material and medical well-being. Whether you agree with this implication or not is not the issue at hand. What is important is that I cannot justify why it is right to provide for the well-being of mankind - you either believe it or you don't, and that's "just knowing."
As a final comment to the rationalists' position, I must denounce their all-too-common practice of deciding their epistemological doctrines to avoid unwanted moral repercussions. If one is to take the extreme position that knowledge is objective and absolute, and that man can know the world as it really is, then one should let the “moral” chips fall where they may. Though I share with Rand many concerns about some of the radical irrationalists, I cannot base my theory of knowledge on possible moral repercussions. Besides, I think that many rationalists, objectivists, and even irrationalists have missed an important point: It is contradictory to the doctrines of irrationality to believe that, except for tautologically true implications, anything necessarily implies anything else. Therefore, there is no particular moral or immoral system implied by the irrationalist epistemology.
I want to dispel the possible impression that the reader may have gotten that I am a misologist, that is, a person who hates logic and reason. Actually, nothing could be further from the truth. It's just that I recognize the limitations of logic and reason. The human experience is simply not reducible to logic (existentialism), and creativity often requires a walk on the wild side. I vehemently resist the dogmatic view that all reality is subject to human logic. For example, many have chosen to reject the notion of an all-powerful God on the reason that it is self-contradictory. They argue that if an all-powerful God exists then it is possible for Him to create a stone He cannot lift. Yes, as the rules of logic stand now, this is clearly a logical paradox. But I propose that this paradox, like Zeno's, only illustrates the limitation of logical analysis. In a similar conundrum, Russell proscribed a caveat against self-referential statements (such as “This sentence is false”) to obviate the logical paradoxes that arise from them I recommend the caveat: Make no inferences based on propositions using “infinities.” Thus, by following this rule we eliminate the logical consideration of “all-powerful” anythings, and we also rule out the logical analysis of infinitely-subdivided intervals. I offer the following epistemological koan: All infinities are illogical. (I will refrain from amplifying what I mean by this for that would defeat the purpose of the koan.) Of course set theory formally deals with infinities in the form of infinite cardinal and ordinal numbers, but these numbers do not follow the ordinary “logic” or rules, of arithmetic. (It may be that all undefined and undefined terms are illogical, inasmuch as to be “logical” is to be explainable. And, in the case of “infinity,” it may be that its definition as a thing that is not finite merely tells us what it is not, and not what it is, even though we supposedly know what “finite” means. Think of it this way: Anytime we try to define a set by use of a negation, we presuppose that we “know” the universal set of objects that we are dealing with. But in this case, that would presuppose that we already know, or have meaning to, the set of all “finites” and “infinites,” which is clearly circular reasoning.)
To recap my assertions: knowledge certainly exists for it is an invention of man. It serves man by offering a metaphorical and subjective characterization of the “known” world. Human knowledge has no absolute status for it is founded on arbitrary definitions. If we change our definitions, we change the way we characterize the world, though presumably the world remains unchanged. That knowledge has no absolute foundation to man is the inevitable result of the pluralistic nature of the world. In a sense, though, knowledge can be said to be “true” when it is understood that knowledge represents the appearance of the world rather than the “real” world itself. Logic has its value as a limited means of gaining knowledge about the world. [One of the limitations of logic (pure deduction) is its inability to deal with synthetic a priori knowledge.] Human empirical knowledge is limited to the meaning the SAS can project “onto the world,” and all meaning is ultimately reducible to the archephors.
Published in: Arizona Journal of Natural Philosophy, Vol. 2, March 1988, pp. 7-14
http://ajnpx.com/html/AJNP.html.
Copyright 1988 by Patrick Reany. All Rights Reserved.
